Five year old cousin with new baby on the way

Hi ladies, just looking for a bit of advice. I have a five year old cousin and I'm 27 weeks pregnant. The five year old recently got a baby sister about 7 months ago and currently can't be babysat with the five year old as the five year old will throw tantrums. Last week I had a prem labour scare while we were minding the five year old and she threw a tantrum because she had to go home. I'm getting quite nervous the closer I get to my due date as the five year old is quite close to myself and my mother who I live with, and she has been known to lash out and hit or be quite rough. We can't compliment her sister in any way or talk about my unborn baby too much as she starts crying and claiming everything as her own. I am quite worried that when the baby's here, he won't be able to be given much attention when the five year old is around which is quite often. Does anyone have any advice or am I just over thinking it all?